MEASUREMENT  OF  MERCURY  VAPOR 

PRESSURE  BY  MEANS  OF  THE  KNUD- 

SEN  PRESSURE  GAUGE 


BY 


CHARLES  FRANCIS  HILL 

^  •.   I- 

A.B.  University  of  Illinois,  1914 
A.M.  University  of  Illinois,  1916 


THESIS 

SUBMITTED  IX  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS 
FOR  THE   DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN 
PHYSICS  IN  THE  GRADUATE  SCHOOL  OF  THE 
UNIVERSITY  OF  ILLINOIS,  1921. 


URBANA,  ILLINOIS 
1922 


Reprinted  from  THE  PHYSICAL  REVIEW,  Vol.  XX,  Second  Series,  No.  3,  September,  1922 


MEASUREMENT  OF  MERCURY  VAPOR 

PRESSURE  BY  MEANS  OF  THE  KNUD- 

SEN  PRESSURE  GAUGE 


BY 


CHARLES  FRANCIS  HILL 

A.B.  University  of  Illinois,  1914 
A.M.  University  of  Illinois,  1916 


THESIS 

SUBMITTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS 
FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN 
PHYSICS  IN  THE  GRADUATE  SCHOOL  OF  THE 
UNIVERSITY  OF  ILLINOIS,  1921. 


URBANA,  ILLINOIS 
1922 


Reprinted  from  THE  PHYSICAL  REVIEW.  Vol.  XX,  Second  Series,  No.  3,  September.  1922 


.•• 


PRESS  OF 

THE  NEW  ERA  PRINTING  COMPANY 
LANCASTCR.  PA. 


[Reprinted  from  THE  PHYSICAL  REVIEW,  N.S.,  Vol.  XX,  No.  3,  September,  1922.] 


MEASUREMENT  OF   MERCURY  VAPOR   PRESSURE   BY 
MEANS   OF  THE   KNUDSEN   PRESSURE   GAUGE. 

BY  CHARLES  F.  HILL. 

SYNOPSIS. 

Vapor  Pressure  of  Mercury,  o  to  35°  C. — The  disagreement  among  the  results 
obtained  by  previous  observers  for  this  range  of  temperature  suggested  the  need 
for  a  direct  determination  of  the  vapor  pressures  with  a  Knudsen  gauge.  Impurities 
were  eliminated  by  numerous  distillations  in  a  system  cut  off  from  the  pump  by  a 
liquid  air  trap,  and  the  slight  amount  of  residual  gas  was  corrected  for.  The  readings 
obtained  at  19  temperatures  lie  near  a  smooth  curve  which,  it  is  believed,  gives 
the  vapor  pressures  to  within  3  per  cent.  The  values  for  o,  10,  20,  and  30°  C.  are, 
respectively,  .000350,  .000775,  .00182  and  .00407  mm.  of  Hg,  considerably  higher 
than  those  obtained  by  Knudsen  in  1909,  but  agreeing  fairly  well  with  Morley's 
results  up  to  15°,  and  at  higher  temperatures  with  values  extrapolated  from  the 
results  of  Ramsey  and  Young. 

HISTORICAL. 

WHILE   engaged  in  experimental  work  in  the  spring  of  1920,  an 
accurate  knowledge  of  the  vapor  pressure  of  mercury  at  room 
temperature  became  of  importance.     On  looking  for  the  values  given  in 
tables  for  temperatures  below  40°  C.  very  little  agreement  among  the 
various  observers  was  found  as  may  be  seen  in  the  following  table. 

TABLE  I. 


T. 

Regnault 
1862. 

Hagen 
1882. 

Hertz 
1882. 

Ramsey  and 
Young  1886. 

Van  der 
Plaats  1886. 

Morley 
1904. 

Knudsen 
1909. 

.000184 

.0005 
.00188 
.00278 
.006 
.0126 

0° 
10° 
20° 
30° 
40° 
50° 
60° 
70° 

.02 
.0268 
.0372 
.053 
.0767 
.112 

.015 
.018 
.021 
.026 
.033 
.042 

.00019 
.0005 
.0013 
.0029 
.0063 
.013 



.00047 
.0008 
.0013 

.0004 
.0008 
.0015 
.003 
.006 
.011 
.021 
.04 

.008 
.015 





1 

In  1886  van  der  Plaats1  published  results  obtained  by  taking  a  large 
number  of  readings  between  o  and  20°  Centigrade.  Values  from  his 
mean  curve  are  usually  given  preference  in  tables.  The  method  was  to 
pass  dry  gas  through  water,  through  sulphuric  acid,  and  then  through 
mercury  until  saturated,  after  which  the  mercury  was  collected  by  gold 
and  pumice  stone  and  weighed.  The  vapor  pressure  was  calculated 
from  the  data  obtained  by  comparison  with  the  vapor  pressure  of  water. 

1  Rec.  Trans.  Chim.,  5.  p.  49,  1886. 


260 


CHARLES   F.    HILL. 


[SECOND 

LSERIES. 


Van  der  Plaats'  readings  show  considerable  variation,  but  are  consistent 
enough  so  that  with  the  number  of  readings  taken  his  results  must  be 
given  considerable  weight.  The  method  would  not  be  expected  to  give 
values  too  high  since  his  chief  error  should  be  loss  of  evaporated  mercury. 
E.  W.  Morley1  in  1904  used  practically  the  same  method  as  van  der 
Plaats  except  that  the  evaporated  mercury  was  measured  by  weighing 
the  sample  before  and  after  evaporation.  Readings  were  taken  at  16, 
30,  40,  50,  60  and  70°  C.,  and  Dalton's  equation 

P  =  abl 

was  used  for  the  calculation  of  the  mean  curve  and  for  extrapolation  to 
o°  C.  Morley 's  readings  at  40,  30  and  16°  C.,  are  from  8  to  20  per  cent, 
below  his  mean  curve  but  at  the  higher  temperatures  his  values  agree 
with  those  given  by  others.  Vapor-pressure  curves  should  have  a 
decreasing  per  cent,  increase  as  the  temperature  increases.  Morley 's 
curve  is  perfectly  uniform  if  the  slope  is  measured  in  this  way,  but  the 
error  in  the  readings  at  low  temperatures  could  easily  account  for  this 
fact.  While  Morley  can  not  claim  a  high  percentage  accuracy  his 
agreement  with  van  der  Plaats  at  low  temperatures,  and  with  the  other 
observers  at  higher  temperatures,  seems  to  indicate  that  the  order  of 
his  values  is  correct. 

The  last  data  of  importance  published  were  those  of  Knudsen2  in  1909. 
An  equation  was  developed  for  the  flow  of  gas  through  a  tube  with  a 
small  opening  over  one  end,  and  an  apparatus  based  on  this  equation 
was  arranged  so  that  the  vapor  pressure  of  mercury  could  be  measured. 
This  equation 


G  = 


+  W" 


Xt 


Fig.  1. 


involves  the  pressure  difference,  the  resistance  of  tube 
and  opening,  the  density  of  the  gas  and  the  time.  G 
is  the  mass  of  the  gas  or  vapor  which  will  flow  through 
the  small  opening  in  an  evacuated  tube,  as  shown  in 
Fig.  i,  with  a  pressure  difference  p'  —  p" .  In  prac- 
tice p"  was  made  zero  by  the  application  of  a  cold 
bath  to  B.  Knudsen 's  results  obtained  by  this  method 
are  about  one  half  as  large  as  those  of  Morley,  and 
also  of  van  der  Plaats,  in  the  region  o  to  40°  C.  The 
fact  that  mercury  requires  an  appreciable  time  for 
evaporation  might  tend  to  produce  such  an  effect  since 
p'  at  the  opening  is  being  relieved  continuously. 


1  Phil.  Mag.,  Vol.  -,  p.  662,  1904. 

2Ann.  der  Physik.  28,  p.  75,  1908-9;  ibid.,  28,  p.  999.  1908-9;  ibid.,  29,  p.  179,  1909. 


VOL.  XX.l 
No.  3.       J 


MEASUREMENT  OF   MERCURY    VAPOR   PRESSURE. 


26t 


EXPERIMENTAL. 

From  the  foregoing  it  seems  desirable  that  there  should  be  additional 
experimental  data  taken  at  ordinary  working  temperatures.  The  Knud- 
sen  pressure  gauge,  in  the  opinion  of  the  writer,  offered  the  most  depend- 
able method  for  such  measurements  since  in  its  action  it  is  independent 
of  the  nature  of  the  gas,  and  also  its  range  is  approximately  that  of  the 
vapor  pressures  to  be  measured.  The  Knudsen  gauge  available  was 
not  arranged  to  be  used  as  an  absolute  manometer,  but  was  calibrated 
by  means  of  an  accurately  constructed  McLeod  gauge.  The  principle 
upon  which  the  Knudsen1  gauge  depends  is  that  the  molecules  of  a 
residual  gas  in  a  partial  vacuum  are  thrown  off  from  a  heated  platinum 
foil,  and  striking  a  light  and  suitably  suspended  vane  exert  a  couple, 
thus  producing  a  deflection  which  may  be  read  by  means  of  an  optical 
system.  The  deflection  for  zero  pressure  of  course  is  zero.  This  fact 
makes  it  possible  to  use  a  McLeod  gauge  for  calibration  purposes,  since 
calibration  curves  may  be  used  with  the  origin  as  an  accurately  deter- 
mined point.  The  McLeod  gauge  may  be  read  quite  accurately  to 
.001  mm.,  or  even  less,  provided  the  glass  and  mercury  are  kept  clean. 

A  special  pyrex  glass  McLeod  gauge  was  constructed- for  the  purpose 
and  fused  directly  to  the  rest  of  the  apparatus  (including  the  Knudsen 
gauge)  which  was  also  of  pyrex  glass.  The  volume  tube  of  the  McLeod 
gauge  was  made  comparatively  large  in  order  to  lessen  friction  and 
surface-tension  effects.  The  gauge  was  found  to  read  consistently  to 
.0005  mm.  if  the  mercury  and  glass  were  kept  clean.  The  apparatus  was 
assembled  as  shown  in  Fig.  2.  The  Knudsen  gauge  A,  and  the  sample 


Fig.  2. 

container  B,  were  rigidly  supported  within  a  tight  asbestos  lined  wooden 
box.     The  apparatus  within   the  box  was  connected   to  the  pumping 

1  Ann.  der  Physik,  32,  pp.  809-842,  1910;    PHYS.  REV.,  12,  pp.  70-80,  1918. 


r SECOND 
262  CHARLES   F.    HILL.  (.SERIES. 

system  and  McLeod  gauge  without  through  a  tube  of  rather  large 
diameter  and  including  a  mercury  trap  C.  The  system  was  evacuated 
by  means  of  a  Langmuir  condensation  pump  supported  by  a  Gaede 
rotary  mercury  pump.  By  continued  pumping  and  with  liquid  air 
surrounding  the  trap  C  the  pressure  was  readily  brought  down  to  about 
.005  mm.  Hg.  It  was  then  further  reduced  by  approximately  equal 
steps.  At  each  step  the  pressure  as  indicated  by  the  McLeod  gauge  was 
accurately  read  simultaneously  with  the  deflection  of  the  Knudsen  gauge, 
while  a  given  constant  current  flowed  through  the  platinum  foil  of  the 
gauge.  In  this  way  data  for  a  calibration  curve  were  obtained.  To 
test  the  consistency  of  the  readings  (for  both  gauges)  sets  of  data  were 
taken  in  which  the  current  supplied  to  the  gauge  had  in  turn  the  values 
.3,  .4,  .5,  .6  ampere.  This  data  when  plotted  on  40  cm.  coordinate 
paper  gave,  for  each  set,  a  smooth  curve,  showing  that  the  two  gauges 
were  at  least  consistent. 

The  sample  of  mercury  was  then  introduced  into  the  container  B 
and  with  liquid  air  surrounding  the  trap  C,  and  the  pumps  running,  the 
mercury  was  distilled  slowly  out  of  the  container  B  and  back  again  by 
heating  first  the  container  and  then  the  rest  of  the  tube.  This  process 
of  distillation  was  carried  out  a  number  of  times.  Warm  water  was 
kept  on  the  sample  to  prevent  loss  of  the  sample  and  condensation  of 
vapors  while  the  entire  tube  within  the  asbestos-lined  box  was  heated 
to  a  temperature  of  250  to  300°  C.  for  several  hours  in  order  to  drive 
the  vapors  out  of  the  walls  of  the  tube.  The  apparatus  was  then  sealed 
off  at  E.  After  allowing  the  box  to  come  to  the  desired  temperature  for 
a  time,  the  total  pressure  was  taken.  The  mercury  was  then  driven  into 
the  container  B,  while  submerged  in  liquid  air,  by  warming  the  rest  of 
the  tube,  and  the  residual  gas  pressure  measured.  The  difference  be- 
tween the  total  and  the  residual  pressures  is  the  vapor  pressure  of  the 
mercury.  Readings  were  thus  taken  at  a  number  of  temperatures  over 
the  range  o  to  35°.  After  completing  the  series  the  tube  was  opened, 
resealed  to  the  pump  and  the  same  process  of  distillation  and  heating 
carried  out  again.  This  method  was  continued  until  minimum  values 
for  the  vapor  pressure  were  obtained  on  three  successive  sets  of  readings. 
The  mercury  was  considered  pure  at  this  point. 

Another  calibration  of  the  Knudsen  gauge  was  now  carried  out,  a 
second  sample  of  mercury,  purified  with  nitric  acid,  was  introduced  and 
the  process  of  distillation  and  heating  was  repeated  eight  times.  The 
tube  was  then  sealed  off  again  at  E  and  readings  were  taken  at  several 
different  temperatures. 

The  four  sets  of  data  obtained  in  this  way  contained  nineteen  indi- 


MEASUREMENT   OF   MERCURY    VAPOR   PRESSURE.  263 

vidual  values  for  the  vapor  pressure  of  mercury  extending  over  the 
temperature  interval  of  —  .7  to  34.9°  Centigrade.  Of  these  values  two 
or  three  differ  from  the  mean  curve  by  about  6  per  cent.,  the  rest  being 
within  3  per  cent,  of  the  curve.  In  the  following  discussion  it  will  be 
shown  that  this  is  about  the  accuracy  that  could  be  expected  from  the 
method. 

The  temperatures  within  the  asbestos-lined  box  were  read  by  means  of 
two  tenth-degree  mercurial  thermometers  placed  at  different  points. 
To  insure  uniform  temperature  the  air  was  caused  to  circulate  within  the 
box  by  a  fan  driven  by  a  motor  without.  The  fan  system  was  supported 
separately  from  the  pier  and  box  to  prevent  jarring  the  Knudsen  gauge. 
The  circulation  of  the  air  was  directed  by  the  bafflers  H.  Two  heating 
coils,  D,  controlled  the  high  temperatures,  while  the  low  temperatures 
were  obtained  by  opening  the  windows  and  cooling  the  room.  In  general 
the  temperatures  were  held  constant,  probably  at  .1  or  very  readily  at 
.2°  C.  Changes  of  .2°  in  the  box  temperature  produced  changes  in  the 
vapor  pressure  that  were  just  detectable  by  the  Knudsen  gauge.  The 
gauge  did  not  register  changes  as  quickly  as  the  thermometers.  The 
Knudsen  gauge  was  read  by  a  lamp  and  scale  at  one  meter  distance. 
In  order  to  hold  the  zero  point,  or  rather  to  hold  the  vane  and  foil  at  a 
constant  distance,  the  scale  was  rigidly  fixed  to  the  floor.  If  the  vane 
became  displaced,  it  could  be  brought  back  to 'its  original  position  by 
merely  restoring  the  zero  on  the  scale.  One  set  of  calibration  curves  was 
used  for  three  sets  of  data,  and  between  each  set  the  calibration  was 
checked  to  make  sure  that  it  remained  constant. 

In  order  to  determine  the  probable  accuracy  of  the  method  some  of 
the  sources  of  error  and  their  probable  magnitude  will  now  be  con- 
sidered. In  the  first  place,  impurities  tend  to  increase  the  vapor  pressure 
in  the  tube,  so  that  this  method  would  be  expected  to  give  values  too 
high.  The  first  sample  gave  minimum  values  for  about  eight  distillations, 
and  since  the  process  of  distillation  was  carried  out  more  than  twenty 
times,  this  error  was  considered  eliminated.  The  second  sample  was 
first  treated  with  nitric  acid  and  then  distilled  eight  times,  hence  we 
were  justified  in  considering  that  the  errors  due  to  impurities  in  this 
sample  were  negligible.  Special  care  was  taken  to  keep  the  McLeod 
gauge  and  the  mercury  in  it  clean  in  order  to  prevent  changes  in  friction. 
It  was  found  that  upon  taking  several  readings  at  the  same  pressure  the 
gauge  could  be  read  to  within  a  total  range  of  =b  2  per  cent.,  except  at 
the  low  pressures  and  these  seemed  to  check  well  with  the  other  readings 
as  shown  by  the  curves.  The  accurately  known  point  on  the  curve  at 
the  origin  helped  to  take  care  of  this  source  of  error.  There  was  a 


264 


CHARLES   F.    HILL. 


[SECOND 
I  SERIES. 


variation  of  3  per  cent,  in  the  Knudsen  gauge  readings,  however,  if  a 
new  set  of  calibration  curves  were  drawn  through  the  same  points,  a 
variation  would  be  obtained  that  would  account  for  most  of  this  error. 
Allowing  for  a  probable  error  of  ±  2  per  cent,  for  temperature  variations 
and  the  same  for  each  of  the  other  sources  of  error,  the  total  probable 
error  should  be  within  about  ±  6  per  cent.  The  fact  that  this  is  the 
range  of  the  actual  readings  seems  to  indicate  that  the  principle  sources 
of  error  have  been  accounted  for  and  the  data  are  about  what  one  should 
expect  from  the  method. 

TABLE  II. 

Third  Run  of  Data. 


I. 

RQ. 

R. 

Deflection. 

Total 
Pressure 
from  Curve. 

Mean. 

Temperature. 

.3 

9.8 

13.0 

3.2 

.00277 

.4 

15.3 

5.5 

.00274 

25° 

.5 

18.0 

8.2 

.00276 

.6 

20.9 

11.1 

.00272 

.00275 

.3 

10.0 

14.32 

4.32 

.00432 

.4 

17.3 

7.3 

.00438 

30.8 

.5 

20.7 

10.7                .00422 

.6 

24.5 

14.5 

.00416 

.00427 

.3 

10.0 

15.0 

5.0 

.0055 

.4 

18.55 

8.55 

.00556 

34.3 

.5 

22.5 

12.5 

.0054 

.6 

26.75 

16.75 

.00514 

.00540 

.3 

9.7 

11.05 

1.35 

.00087 

.4 

12.02 

2.32 

.00088 

.5 

13.19 

3.49 

.00089 

11.6 

.6 

14.5 

4.8 

.00088 

.00088 

.3 

10.2 

10.8 

.6 

.00033 

.4  , 

11.17 

.97 

.00036 

-.7 

.5 

11.7 

1.5 

.00036 

.6 

12.35 

2.15 

.00036 

.00035 

s'    '.  -  .• 

Residual 

•   •  'i  '        •                 *  *• 

Pressure 

from  Curve. 

.3 

10.15 

deflection  hardly  perceptible 

.4 

10.19 

.04 

.00002 

.5 

10.23 

.08 

.00002 

.6 

10.28 

.13 

.00002 

.00002 

One  set  of  the  actual  readings  taken  is  given  in  Table  II.  which  con- 
stituted the  third  run  in  the  first  series.     The  total  pressure  for  a  given 


VOL.  XX.1 
No.  3. 


MEASUREMENT  OF   MERCURY    VAPOR   PRESSURE. 


265 


temperature  is  given  in  the  fifth  column  for  different  values  of  current 
flowing  through  the  Knudsen  gauge.  The  mean  of  these  is  recorded 
in  the  sixth  column.  At  the  bottom  of  the  table  is  the  data  giving  the 
residual  gas  pressure.  Obviously  the  total  pressure  less  this  gas  pressure 
is  the  vapor  pressure  of  mercury.  Table  II.  contains  the  data  for  the 
vapor  pressure  of  mercury  at  five  different  temperatures.  A  second 
series,  in  which  a  new  sample  of  mercury  cleaned  with  nitric  acid  as 
noted  earlier,  gave  values  of  the  vapor  pressure  for  additional  tempera- 
tures. Together  the  two  series  gave  nineteen  values  extending  over  a 
range  in  temperature  from  —  .7  to  34.9°  C.  which  are  collected  in 
Table  III.  The  corresponding  graph  is  shown  in  Fig.  3.  The  points 


Fig.  3. 
TABLE  III. 

Values  for  the  Vapor  Pressure  of  Mercury  at  Various  Temperatures. 


Temperature. 


Pressure 
mm.  Mercury. 


Temperature. 


Pressure 
mm.  Mercury. 


-.7° 00033 

5.7 00055 

11.4 00092 

11.6 00086 

11.6 000815 

13.0 00097 

20.3 00187 

22.8 00230 

23.0 00224 

23.0  .  .    .00235 


24.0° 00262 

25.0 00273 

25.6    00292 

26.8 003145 

28.6 0037 

29.9    004075 

30.8    00425 

34.3    00538 

34.9  ..  .    .00575 


all  lie  well  upon  a  smooth  curve.     In  Table  IV.  the  vapor  pressure  of 
mercury  in  mm.  is  given  for  2-degree  intervals  taken  from  the  curve. 

In  conclusion,  the  author  wishes  to  thank  Professor  A.  P.  Carman  for 
the  use  of  the  facilities  of  the  laboratory,  and  also  to  thank  Professor 


266                                                      CHARLES  F.    HILL. 

C.  T.  Knipp  for  the  interest  he  has  taken  in  the  work  and  for  the  many 
suggestions  offered. 

TABLE  IV. 

Values  for  Each  2°  as  Taken  from  Smooth  Curve  Through  the  Points. 

0.0° 000350  mm.  Hg.  22.0° 00214  mm.  Hg. 

2.0 000412  24.0    00234 

4.0 000487  26.0   003 

6.0 000572  28.0 0035 

8.0 000662  30.0    00407 

10.0 000775  32.0 00467 

12.0 000895  34.0 00535 

14.0 00105  36.0    00607 

16.0 00126  38.0    00695 

18.0 .00150  40.0 008 

20.0 00182 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS. 


VITA 

Charles  Francis  Hill  received  his  early  education 
in  the  public  schools  of  Illinois,  and  his  college  pre- 
paratory work  in  the  Eastern  Illinois  State  Normal 
School  from  which  he  graduated  in  1911.  He  then 
entered  the  University  of  Illinois,  from  which  he  re- 
ceived the  degree  of  A. B.,  in  1914.  From  1914  to  1921 
he  has  been  an  assistant  in  physics  at  the  University 
of  Illinois,  doing  part-time  graduate  work,  having  re- 
ceived the  degree  of  A.M.,  in  1916. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
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Makers 

Syracuse,  N.  Y. 

PM.JAM  21,1308 


53028! 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


